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Adaptive Dual Covariance Steering with Active Parameter Estimation

Jacob W. Knaup, Panagiotis Tsiotras

Abstract

This work examines the optimal covariance steering problem for systems subject to unknown parameters that enter multiplicatively with the state and control, in addition to additive disturbances. In contrast to existing works, the unknown parameters are modeled as random variables and are estimated online. This work proposes the utilization of recursive least squares estimation for efficient parameter identification. A dual control problem is formulated in which the effect of the planned control policy on the parameter estimates is modeled and optimized for. The parameter estimates are then used to modify the pre-computed control policy online in an adaptive control fashion. Finally, the proposed approach is demonstrated in a vehicle control example with closed-loop parameter identification.

Adaptive Dual Covariance Steering with Active Parameter Estimation

Abstract

This work examines the optimal covariance steering problem for systems subject to unknown parameters that enter multiplicatively with the state and control, in addition to additive disturbances. In contrast to existing works, the unknown parameters are modeled as random variables and are estimated online. This work proposes the utilization of recursive least squares estimation for efficient parameter identification. A dual control problem is formulated in which the effect of the planned control policy on the parameter estimates is modeled and optimized for. The parameter estimates are then used to modify the pre-computed control policy online in an adaptive control fashion. Finally, the proposed approach is demonstrated in a vehicle control example with closed-loop parameter identification.
Paper Structure (9 sections, 3 theorems, 24 equations, 4 figures, 1 table)

This paper contains 9 sections, 3 theorems, 24 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Covariance Steering Controller Design
  4. Existing Methods
  5. Proposed Approach
  6. Tractable Formulation
  7. Sample Average Approximation
  8. Numerical Example
  9. Conclusion

Key Result

Lemma 1

The solution to Problem prob:wbls is given by for $k = 0, 1, \dots, N-1$, where $\hat{p}_0 = \bar{p}$ and $P_0 = P$.

Figures (4)

  • Figure 1: Kinematic bicycle model in curvilinear coordinates.
  • Figure 2: Parameter distributions.
  • Figure 3: Sampled vehicle trajectories.
  • Figure 4: Terminal constraint visualization.

Theorems & Definitions (9)

  • Definition 1: Adaptive Control unbehauen2000adaptiveseborg1986adaptiveisermann1982parameter
  • Definition 2: Adaptive Dual Control unbehauen2000adaptivefilatov2000surveybar1974dualmesbah2018stochastic
  • Lemma 1: Recursive Least Squares islam2019recursive
  • proof
  • Lemma 2: liu2022optimal
  • proof
  • Remark 1
  • Theorem 1
  • proof